Reverse concatenated encoding and decoding

ABSTRACT

Methods and systems for transmitting and receiving data include reverse concatenated encoding and decoding. Reverse concatenated decoding includes inner decoding the encoded stream with an inner decoder that uses a low-complexity linear-block code to produce an inner-decoder output stream, outer decoding the inner-decoder output stream with an outer decoder that uses a low-density parity-check code to produce an information stream, and iterating extrinsic bit reliabilities from the outer decoding for use in subsequent inner decoding to improve decoding performance.

RELATED APPLICATION INFORMATION

This application claims priority to provisional application Ser. No.61/375,313 filed on Aug. 20, 2010, incorporated herein by reference.

BACKGROUND

1. Technical Field

The present invention relates to forward error correction (FEC) forhigh-speed serial optical transport and, in particular, to systems andmethods for reverse-concatenated encoding and decoding with low densityparity-check codes.

2. Description of the Related Art

In the recent years, with the rapid growth of data-centric services andthe general deployment of broadband access networks, the densewavelength division multiplexing (DWDM) network has been upgraded from10 Gb/s per channel to more spectrally efficient 40 Gb/s or 100 Gb/s perchannel systems and beyond. 100 Gb/s Ethernet (100 GbE) has recentlybeen standardized. As the communication rate over a fiber-optics channelincreases, transmission becomes increasingly sensitive to errors due tovarious linear and nonlinear channel impairments such as chromaticdispersion, polarization mode dispersion, and fiber nonlinearities. TheShannon limit for a noise-influenced channel describes a maximum amountof data that can be transmitted reliably with a specified bandwidth—itis therefore helpful to have robust codes and modulation schemes thatclosely approach the Shannon limit without imposing too highrequirements in terms of implementation cost and complexity.

SUMMARY

A method for receiving data is shown that includes receiving an encodeddata stream and decoding the encoded data stream with a reverseconcatenated decoder, said decoding. Said decoding includes innerdecoding the encoded stream with an inner decoder that uses alow-complexity linear-block code to produce an inner-decoder outputstream, outer decoding the inner-decoder output stream with an outerdecoder that uses a low-density parity-check code to produce aninformation stream, and iterating extrinsic bit reliabilities from saidouter decoding for use in subsequent inner decoding to improve decodingperformance.

A method for transmitting data is shown that includes receiving aninformation stream, encoding the information stream with a reverseconcatenated encoder to enable iterated reliability reverse concatenateddecoding, and transmitting the reverse concatenated encoded stream. Saidencoding includes outer encoding the information stream with an outerencoder that uses a low-density parity-check (LDPC) code and innerencoding the LDPC-encoded stream with an inner encoder that uses alow-complexity block code.

A receiver is shown that includes a detector configured to receive areverse concatenated encoded signal and pass the signal to a reverseconcatenated decoder and one or more reverse concatenated decodersconfigured to decode the reverse concatenated encoded signal to producean information stream. Each reverse concatenated decoder includes aninner decoder configured to decode the reverse concatenated encodedsignal with a low-complexity linear-block code and to produce aninner-decoder output stream and an outer decoder configured to decodethe inner-decoder output stream using a low-density parity-check code toproduce an information stream and further configured to iterateextrinsic bit reliabilities to the inner decoder to improve decodingperformance.

A transmitter is shown that includes one or more reverse concatenatedencoders configured to encode an information stream and produce areverse concatenated encoded stream to enable iterated reliabilityreverse concatenated decoding and one or more modulators configured tomodulate the reverse concatenated encoded streams onto a carrier fortransmission. Said reverse concatenated encoders include an outerencoder configured to encode an information stream using a low-densityparity-check (LDPC) code and an inner encoder configured to encode theLDPC-encoded stream with a low-complexity linear-block code.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1 shows a block diagram illustrating an optical transmission systemaccording to the present principles.

FIG. 2 shows a block/flow diagram that illustrates a Gallaghersum-product method for decoding low-density parity-check (LDPC) codesaccording to the present principles.

FIG. 3 shows a block diagram illustrating an optical transmitter thatemploys reverse concatenated codes according to the present principles.

FIG. 4 shows a block diagram illustrating a reverse concatenated encoderaccording to the present principles.

FIG. 5 shows a block diagram illustrating an optical receiver thatdecodes reverse concatenated codes according to the present principles.

FIG. 6 shows a block diagram illustrating a reverse concatenated decoderaccording to the present principles.

FIG. 7 shows a block/flow diagram illustrating a system/method fortransmitting data using reverse concatenated codes according to thepresent principles.

FIG. 8 shows a block/flow diagram illustrating a system/method forreceiving and decoding data using reverse concatenated codes accordingto the present principles.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Through the use of concatenated codes, target net coding gains can beachieved even with reasonably short low-density parity-check (LDPC)codes of low girth (e.g., girth of 6 or 8). However, short LDPC codes oflow girth and reasonable LDPC decoder complexity (having, e.g., columnweight 3 in a min-sum-with-correction-term decoder) exhibit error floorsin the region of interest for optical communications. Using a girth 6LDPC code as an inner code and a Reed-Soloman code as an outer code, theerror floor may be eliminated, but the net coding gain is far below thatof large-girth LDPC codes.

To achieve the bit error rate (BER) performance of large-girth LDPCcodes using reasonably short concatenated codes, the present principlesmake use of an LDPC code as an outer code and, e.g., a Reed-Muller (RM)or Hocquenghem, Bose, Ray-Chaudhuri (BCH) code as an outer code. BecauseBCH and RM codes can be efficiently decoded using maximum a posteriori(MAP) probability, the reliable bit log-likelihood ratios (LLRs) can beforwarded to an outer LDPC decoder. Although BCH and RM codes aredescribed herein, it is contemplated that any low-complexity block codecould be used according to the present principles. With reasonably shortLDPC codes, one can achieve BER performance and net coding gainscomparable to large-girth LDPC codes using reverse concatenation.

Embodiments described herein may be entirely hardware, entirely softwareor including both hardware and software elements. In a preferredembodiment, the present invention is implemented in software, whichincludes but is not limited to firmware, resident software, microcode,etc.

Embodiments may include a computer program product accessible from acomputer-usable or computer-readable medium providing program code foruse by or in connection with a computer or any instruction executionsystem. A computer-usable or computer readable medium may include anyapparatus that stores, communicates, propagates, or transports theprogram for use by or in connection with the instruction executionsystem, apparatus, or device. The medium can be magnetic, optical,electronic, electromagnetic, infrared, or semiconductor system (orapparatus or device) or a propagation medium. The medium may include acomputer-readable storage medium such as a semiconductor or solid statememory, magnetic tape, a removable computer diskette, a random accessmemory (RAM), a read-only memory (ROM), a rigid magnetic disk and anoptical disk, etc.

A data processing system suitable for storing and/or executing programcode may include at least one processor coupled directly or indirectlyto memory elements through a system bus. The memory elements can includelocal memory employed during actual execution of the program code, bulkstorage, and cache memories which provide temporary storage of at leastsome program code to reduce the number of times code is retrieved frombulk storage during execution. Input/output or I/O devices (includingbut not limited to keyboards, displays, pointing devices, etc.) may becoupled to the system either directly or through intervening I/Ocontrollers.

Network adapters may also be coupled to the system to enable the dataprocessing system to become coupled to other data processing systems orremote printers or storage devices through intervening private or publicnetworks. Modems, cable modern and Ethernet cards are just a few of thecurrently available types of network adapters.

Referring now to the drawings in which like numerals represent the sameor similar elements and initially to FIG. 1, an optical communicationssystem is shown comprising a transmitter 100 and a receiver 101. Thetransmitter encodes a plurality of data signals at the concatenatedencoder block 102. A concatenated encoder may include a plurality ofencoders arranged serially, as described in detail below. The encodedstream is then interleaved at interleaving block 104. The mapping andmodulation block 106 then assigns bits of the interleaved signal to aniterative polarization modulation constellation, associating the bits ofthe interleaved data signals with the points on an iterative polarquantization (IPQ) constellation or quadrature amplitude modulation QAMconstellation. The transmitter 100 then sends the signal to receiver 101over an optical medium 107, which may include periodically deployederbium doped fiber (EDF) amplifiers to maintain the signal strength.Other embodiments include the use of Raman and hybrid Raman/EDFamplifiers. Although embodiments described herein are directed tooptical media and systems, it is contemplated that the presentprinciples may be employed in any communications system. Receiver 101detects symbols in the IPQ constellation at block 108. A backpropagationand equalization block 110 performs coarse digital backpropagation andturbo equalization to compensate for channel impairments such aspolarization mode dispersion, chromatic dispersion, and fibernon-linearities. The signals are then de-interleaved and decoded atconcatenated decoding block 112, which uses decoders of the same type asused in concatenated encoder 102 arranged in the opposite order, toproduce the original data signals.

The concatenated encoders 102 and decoders 112 make use of LDPC codes toprovide error correction that brings the transmissions close to thechannel capacity. Several definitions will be employed below to describeLDPC decoding. A regular (n, k) LDPC code is a linear block code whoseparity-check matrix H includes exactly W_(c) 1s per column and exactlyW_(r)=W_(c)(n|(n−k)) 1s per row, where W_(c)<<n−k). The n termrepresents the total number of bits in a coded word produced by the LDPCcode, while the k term represents the number of information bits encodedby the code word. Choice of parity matrix can greatly affect theeffectiveness of the LDPC code. Decoding of LDPC codes is based on asum-product algorithm (SPA), which is an iterative decoding algorithmthat iterates extrinsic probabilities forward and back between variable-and check-nodes of bipartite (e.g., Tanner) graph representations of theparity-check matrix H. The Tanner graph of an LDPC code is drawnaccording to the following rule: check node c is connected to variablenode v whenever element h_(cv) in H is a 1. For variable-node v andcheck-node c the neighborhoods N(v) and N(c) are defined as the set ofcheck-nodes and variable nodes connected to the variable nor or checknode (respectively) in question.

Referring now to FIG. 2, an exemplary Gallagher SPA is shown. Block 202initializes messages L_(v→c) to be sent from variable-node v tocheck-node c as channel log-likelihood ratios (LLRs) L_(ch)(v). ChannelLLRs are defined byL _(ch)(v)=log [P(v=0|y)/P(v=1|y)].where y is the channel sample and the probability terms refer to thelikelihood of the channel sample being a 0 or a 1 respectively. Forexample, for asymmetric additive white Gaussian noise (AWGN) channels,L _(ch)(v)=log(σ₁/σ₂)−(y−μ ₀)²/2σ₀ ²+(y−μ _(i))²/2σ₁ ²,where the values of μ and σ are determined by propagating a trainingsequence, while for a symmetric AWGN channel,L _(ch)(v)=2y/σ ².

Block 203 begins check-node updating by initializing a counter c for thecheck-nodes. Block 204 computes the messages L_(c→v) from thecheck-nodes to the variable-nodes as a new summation over theneighborhood of check-node c excluding the variable-node v:

$L_{c\rightarrow v} = {\underset{{N{(c)}}\backslash{\{ v\}}}{\oplus}{L_{v\rightarrow c}.}}$The ⊕ operator is defined for the Gallagher SPA by

${{L_{1} \oplus L_{2}} = {\prod\limits_{k = 1}^{2}\;{{{sign}\left( L_{k} \right)}{\phi\left( {\sum\limits_{k = 1}^{2}{\phi\left( {L_{k}} \right)}} \right)}}}},$where φ(x)=−log(tan h(x/2)). Block 206 then increments the counter c andblock 208 checks whether c has reached n−k. If not, processing returnsto block 204 to handle the next check-node. If so, processing goes on toupdate the variable-nodes using a v-node update rule.

Block 210 calculates a new L_(v→c) for each variable-node v as

$L_{v\rightarrow c} = {{L_{ch}(v)} + {\sum\limits_{{N{(v)}}\backslash{\{ c\}}}L_{c\rightarrow v}}}$for every c node where h_(cv)=1. Block 211 updates the log-likelihoodratio for variable-node v (corresponding to the likelihood of a givenbit being one or zero) for all v as:

${L(v)} = {{L_{ch}(v)} + {\sum\limits_{N{(v)}}{L_{c\rightarrow v}.}}}$If L(v)<0, a decision {circumflex over (v)} corresponding to thetransmitted bit value of v is set to 1, otherwise {circumflex over(v)}=0. Decision block 214 determines whether {circumflex over(v)}H^(T)=0. If so, processing ends at block 216. Otherwise processingreturns to check-node updating at block 203.

The Gallagher SPA's check-node update rule involves both a logarithm anda hyperbolic tangent, making it computationally intensive. As such,approximations are used to reduce the processing burden. One suchapproximation is the min-sum-plus-correction-term approximation. It canbe shown that the ⊕ operator can also be calculated as:

${L_{1} \oplus L_{2}} = {{\alpha\left\lbrack {{\prod\limits_{k = 1}^{2}\;{{{sign}\left( L_{k} \right)}{\min\left( {{L_{1}},{L_{2}}} \right)}}} + {c\left( {x,y} \right)}} \right\rbrack}.}$The c(x,y) term denotes a correction factor defined by:c(x,y)=log [1+exp(−|x+y|)]−log [1+exp((−|x−y−)],which may be implemented as a lookup table (LUT). The α term representsan attenuation factor. In tests, it has been found that themin-sum-plus-correction-term decoding suffers negligible performanceloss as compared to Gallagher SPA. Min-sum decoding with an optimalattenuation factor of α=0.8 (for Gaussian channels) performs the same asGallagher SPA.

Referring now to FIG. 3, a detailed view of transmitter 100 is shown. 2mdata signals feed into the transmitter. The data signals are dividedinto m signals to be put on an x polarization and m signals for a ypolarization. FIG. 3 illustrates two separate branches, one for each ofthe respective polarization, and m signals for each branch. Although thebranches are described herein as having equal numbers of input datasignals, the branches may also accept different numbers of inputs. Thedata streams are encoded at reverse concatenated encoders 302 usingdifferent reverse concatenated codes having code ratesR_(i)=K_(i)/H(iε{x,y}), where K_(i) denotes the number of informationsymbols used in the binary reverse concatenated code corresponding toeach polarization and N denotes the codeword length.

The outputs of the encoders are then bit-interleaved by m×Nbit-interleavers 304, where the sequences are written row-wise and readcolumn-wise from a block-interleaver. The output of the interleavers 304is sent in respective bit-streams m bits at a time instant i, to mappers306.

The mappers 306 map each m bits into a 2^(m)-ary QAM signalconstellation or IPQ constellation point based on a lookup table. Themappers 306 assign bits to constellation points in polar coordinatess_(l)=(I_(l),Q_(l))=|s_(l)exp(jφ_(l)), where I and Q represent thein-phase and quadrature channels respectively, and with the mappedcoordinates from the mapper 306 being used as the inputs of an I/Qmodulators 308. A laser 310 produces a carrier beam that is split atpolarization beam splitter 311 into two orthogonal polarizations. TheI/Q modulators 308 modulate the constellation points onto theorthogonally polarized carrier beams. The beams from the respectivebranches of the transmitter 100 are then combined in beam combiner 312before being transmitted on an optical fiber. Because the combined beamsoccupy polarizations that are orthogonal with respect to one another,they can be combined without loss of information.

Referring now to FIG. 4, a detailed view of the reverse concatenatedencoder 302 is shown. The information stream is received by outer LDPCencoder 402 which uses, for example, an LDPC code having girth 8 andcolumn weight 3. This encoded information passes to an interleaver 404before being encoded again by an inner encoder 406 that uses, forexample, a BCH or RM code.

Referring now to FIG. 5, a detailed view of the receiver 101 is shown. Acarrier beam is received from an optical fiber and is split atpolarization beam splitter 502 into two orthogonal polarizations.Detectors 504 demodulate the beams to produce I and a Q signal estimatesby sampling their respective signals. Although detectors 504 areadvantageously implemented as coherent detectors, it is contemplatedthat other sorts of detector might be used. In embodiments that employcoherent detection, a local laser source (not shown) is used to providethe detectors 504 with a local reference that allows them to quicklydistinguish between the orthogonal polarizations and extract theinformation.

The I and Q signals produced by the detectors 504 then pass to module506 which performs digital backpropagation and MAP equalization, wherevarious channel impairments are corrected. The data stream is thenpassed to bit log likelihood ratio (LLR) modules 508. The bit LLRmodules 508 determine the bit LLRs from symbol LLRs. The bit LLR modules508 include a lookup table that stores the same constellationinformation as the lookup table at the transmitter, allowing the bit LLRmodules 508 to convert symbols to bit sequences. The symbol LLRs aredefined as λ(s)=log [P(s|r)/P(s₀|r)], where s=(I_(i)Q_(i)) andr=(r_(I),r_(Q)) denote the transmitted signal constellation point andreceived symbol at time instance i respectively, and s₀ represents thereference symbol, and are determined in block 506. Each symbol s isrepresented by a binary representation c=(c₁, c₂, . . . , c_(J)), whereeach bit c_(i) of the observed symbol s is shown. Bit LLRs are definedusing the bit LLRs as:

${{L\left( c_{i} \right)} = {\log\frac{\sum\limits_{{c:c_{i}} = 0}{{\exp\left( {\lambda(q)} \right)}{\exp\left( {\sum\limits_{{{c:c_{ji}} = 0},{j \neq i}}{L_{a}\left( c_{j} \right)}} \right)}}}{\sum\limits_{{c:c_{i}} = 1}{{\exp\left( {\lambda(q)} \right)}{\exp\left( {\sum\limits_{{{c:c_{ji}} = 0},{j \neq i}}{L_{a}\left( c_{j} \right)}} \right)}}}}},$where L_(a)(c_(j)) is the a priori information determined from thereverse concatenated decoder's extrinsic LLRs. L(c_(i)) calculates thelogarithm of the ratio of a probability that each bit c_(i) is zero, anda probability that each bit is one. In the nominator, the summation isdone over all symbols q having a zero at position I, while in thedenominator summation is performed over all symbols q having a one atposition i. By iterating extrinsic reliabilities between MAP detector506 and reverse concatenated decoder 510, overall performance isimproved.

The bit LLR modules 508 each produce m bit LLRs which are processed by mreverse concatenated decoders 510. Bit reliabilities for the reverseconcatenated decoders 510 are calculated from symbol reliabilities. Toimprove bit error rate (BER) performance, EXIT chart analysis is used inselecting of LDPC codes and extrinsic reliabilities are iterated betweenmaximum a posteriori (MAP) equalizer 506 and reverse concatenateddecoders 510 in turbo equalization fashion until convergence or until apredetermined number of iterations has been reached. The MAP equalizersform a part of the turbo equalizer in block 506. One advantageousembodiment of a MAP equalizer uses the Bahl-Cocke-Jelinek-Raviv (BCJR)method. Another uses a soft-output viterbi method (SOVA) forequalization. It is contemplated that any suitable implementation of aMAP equalizer may be employed. The reverse concatenated decoders 510then produce the original 2m data signals as output and feed backextrinsic LLR information to the turbo equalizers in block 506. Theequalizers can compensate for nonlinear polarization mode dispersion aswell.

Referring now to FIG. 6, a detailed view of reverse concatenateddecoders 510 is shown. Encoded data is received by the inner decoder 602which employs, for example, a BCH or RM decoder. If BCH is used, theinner decoder 602 may be implemented as a soft MAP decoder, and if RM isused, the inner decoder 602 may be implemented based on Ashikmin-Lytsinsoft-decision decoding. The output of the inner decoder 602 isdeinterleaved by deinterleaver 604 and then LDPC decoded by the outerLDPC decoder 606. To improve performance of the reverse concatenateddecoder 510, extrinsic LLRs are iterated between the inner BCH/RMdecoder 602 and outer LDPC decoder 606. For example, the extrinsic LLRof the j^(th) bit for a BCH decoder 602 in the k^(th) iteration isdetermined by:L _(BCH,e)(c _(j) ^((k)))=L _(LDPC)(c _(j) ^((k)))−L _(LDPC)(c _(j)^((k−1))),where L_(LDPC)(c_(j)) is an LLR corresponding to bit c_(j) after LDPCdecoding, while the indices k and k−1 denote a current and a previousiteration respectively.

Referring now to FIG. 7, a system/method for encoding and modulatingdata for transmission using reverse concatenated codes with QAMmodulation is shown. These methods provide for very high transmissionrates, in excess of 1 Tb/s. A plurality of data streams are encoded atblock 701 using a reverse concatenated encoder as described above inreference to FIG. 6. This includes a step of LDPC encoding 702 the datastream using an inner LDPC encoder. Block 704 then interleaves the LDPCencoded data stream before block 706 encodes the interleaved streamswith, e.g., a BCH or RM encoder.

Block 708 takes the reverse concatenated encoded streams and interleavesthem, preparing the streams for transmission onto two polarizationstreams. The data streams intended for transmission over correspondingpolarization streams are mapped by block 710 to QAM constellationsymbols, providing I and Q values that identify particular symbols. TheI and Q values for each set of symbols are used to modulate the symbolsonto orthogonally polarized carrier beams via quadrature amplitudemodulation by block 712 onto respective polarized orthogonal carrierbeams. The polarized carrier beams may then be combined into a singlebeam by block 714, such that the two polarizations do not interfere withone another during transmission. The combined carrier beam can then betransmitted over an optical fiber to its destination.

Referring now to FIG. 8, a system/method for receiving and decodingreceived data is shown. A combined carrier beam is received from anoptical transmission fiber at block 800 and is then split into twoorthogonal polarizations at block 802. QAM symbols are then detected andextracted from the carrier beams at block 804. It is contemplated thatany method of detection could be used, but for the purposes of exampleand discussion coherent detection is used herein.

Channel distortions are compensated for using turbo equalization inblock 806. The bit LLRs used for reverse concatenated decoding arecalculated at block 808 from symbol LLRs. Block 809 then performsreverse concatenated decoding. Block 810 employs, for example, an innerBCH or RM decoder to perform MAP decoding. This data is thendeinterleaved at block 812 before being LDPC decoded by an outer LDPCdecoder at block 814. The bit LLRs from block 808 are used to LDPCdecode the encoded data according to, for example,min-sum-with-correction-term as discussed above. Extrinsic LLRinformation is passed back to block 806 from the LDPC decoding 814 to beused in subsequent turbo equalization iterations.

Reverse concatenated codes according to the present principles showsubstantial performance gains. For example, a reverse concatenated codeusing a (16935,14819) LDPC code and a (128,120) BCH code outperforms thecorresponding turbo-product counterpart with a Chase II decodingalgorithm by 0.88 dB at a BER of 10⁻⁹. The net coding gain of the samereverse concatenated code is 9.56 dB at the same BAR, while the netcoding gain at a BER of 10⁻¹³ is 11.32 dB. Furthermore, the exemplaryreverse concatenated code is only 0.2 dB away from a girl 12 LDPC codeof length 345165.

Having described preferred embodiments of a system and method forreduced-complexity LDPC decoding (which are intended to be illustrativeand not limiting), it is noted that modifications and variations can bemade by persons skilled in the art in light of the above teachings. Itis therefore to be understood that changes may be made in the particularembodiments disclosed which are within the scope of the invention asoutlined by the appended claims. Having thus described aspects of theinvention, with the details and particularity required by the patentlaws, what is claimed and desired protected by Letters Patent is setforth in the appended claims.

What is claimed is:
 1. A method for receiving data, comprising:receiving an encoded data stream; and decoding the encoded data streamwith a reverse concatenated decoder, said decoding comprising: innerdecoding the encoded stream with a soft maximum a posteriori innerdecoder that uses a low-complexity linear-block code to produce aninner-decoder output stream; outer decoding the inner-decoder outputstream with an outer decoder that uses a low-density parity-check codehaving a girth between 6 and 8 and a column weight of 3 to produce aninformation stream; and iterating extrinsic log-likelihood ratios fromsaid outer decoding for use in subsequent inner decoding to improvedecoding performance.
 2. The method of claim 1, wherein the innerdecoder uses a Bose-Chaudhuri-Hocquenghem (BCH) code.
 3. The method ofclaim 1, wherein the inner decoder uses a Reed-Muller code.
 4. Themethod of claim 1, wherein decoding further comprises deinterleaving theinner-decoder output stream before outer decoding.
 5. A method fortransmitting data, comprising: receiving an information stream; encodingthe information stream with a reverse concatenated encoder to enableiterated reliability reverse concatenated decoding, said encodingcomprising: outer encoding the information stream with an outer encoderthat uses a low-density parity-check (LDPC) code having a girth between6 and 8 and a column weight of 3; and inner encoding the LDPC-encodedstream with an inner encoder that uses a low-complexity block code; andtransmitting the reverse concatenated encoded stream.
 6. The method ofclaim 5, wherein the inner encoder uses a Bose-Chaudhuri-Hocquenghem(BCH) code.
 7. The method of claim 5, wherein the inner encoder uses aReed-Muller code.
 8. The method of claim 5, wherein the encoding furthercomprises interleaving the LDPC-encoded stream before inner encoding. 9.A receiver, comprising: a detector configured to receive a reverseconcatenated encoded signal and pass the signal to a reverseconcatenated decoder; and one or more reverse concatenated decodersconfigured to decode the reverse concatenated encoded signal to producean information stream, each comprising: a soft maximum a posterioriinner decoder configured to decode the reverse concatenated encodedsignal with a low-complexity linear-block code and to produce aninner-decoder output stream; and an outer decoder configured to decodethe inner-decoder output stream using a low-density parity-check codehaving a girth between 6 and 8 and a column weight of 3 to produce aninformation stream and further configured to iterate extrinsiclog-likelihood ratios to the inner decoder to improve decodingperformance.
 10. The receiver of claim 9, wherein the inner decoder usesa Bose-Chaudhuri-Hocquenghem (BCH) code.
 11. The receiver of claim 9,wherein the inner decoder uses a Reed-Muller code.
 12. A transmitter,comprising: one or more reverse concatenated encoders configured toencode an information stream and produce a reverse concatenated encodedstream to enable iterated reliability reverse concatenated decoding,each comprising: an outer encoder configured to encode an informationstream using a low-density parity-check (LDPC) code having a girthbetween 6 and 8 and a column weight of 3; and an inner encoderconfigured to encode the LDPC-encoded stream with a low-complexitylinear-block code; and one or more modulators configured to modulate thereverse concatenated encoded streams onto a carrier for transmission.13. The transmitter of claim 12, wherein the inner encoder uses aBose-Chaudhuri-Hocquenghem (BCH) code.
 14. The transmitter of claim 12,wherein the inner encoder uses a Reed-Muller code.
 15. The transmitterof claim 12, wherein the one or more reverse concatenated encoders eachfurther comprise an interleaver configured to interleave theLDPC-encoded stream and to output the interleaved stream to the innerencoder.